1
JEE Main 2020 (Online) 9th January Evening Slot
+4
-1
A uniformly thick wheel with moment of inertia I and radius R is free to rotate about its centre of mass (see fig). A massless string is wrapped over its rim and two blocks of masses m1 and m2 (m1 $$>$$ m2) are attached to the ends of the string. The system is released from rest. The angular speed of the wheel when m1 descents by a distance h is : A
$${\left[ {{{2\left( {{m_1} + {m_2}} \right)gh} \over {\left( {{m_1} + {m_2}} \right){R^2} + I}}} \right]^{{1 \over 2}}}$$
B
$${\left[ {{{{m_1} + {m_2}} \over {\left( {{m_1} + {m_2}} \right){R^2} + I}}} \right]^{{1 \over 2}}}gh$$
C
$${\left[ {{{\left( {{m_1} - {m_2}} \right)} \over {\left( {{m_1} + {m_2}} \right){R^2} + I}}} \right]^{{1 \over 2}}}gh$$
D
$${\left[ {{{2\left( {{m_1} - {m_2}} \right)gh} \over {\left( {{m_1} + {m_2}} \right){R^2} + I}}} \right]^{{1 \over 2}}}$$
2
JEE Main 2020 (Online) 9th January Morning Slot
+4
-1 Three solid spheres each of mass m and diameter d are stuck together such that the lines connecting the centres form an equilateral triangle of side of length d. The ratio I0/IA of moment of inertia I0 of the system about an axis passing the centroid and about center of any of the spheres IA and perpendicular to the plane of the triangle is :
A
$${{13} \over {23}}$$
B
$${{23} \over {13}}$$
C
$${{15} \over {13}}$$
D
$${{13} \over {15}}$$
3
JEE Main 2020 (Online) 8th January Evening Slot
+4
-1
A uniform sphere of mass 500 g rolls without slipping on a plane horizontal surface with its centre moving at a speed of 5.00 cm/s. Its kinetic energy is :
A
8.75 × 10–3 J
B
1.13 × 10–3 J
C
8.75 × 10–4 J
D
6.25 × 10–4 J
4
JEE Main 2020 (Online) 8th January Morning Slot
+4
-1
Consider a uniform rod of mass M = 4m and length $$\ell$$ pivoted about its centre. A mass m moving with velocity v making angle $$\theta = {\pi \over 4}$$ to the rod's long axis collides with one end of the rod and sticks to it. The angular speed of the rod-mass system just after the collision is :
A
$${{3\sqrt 2 } \over 7}{v \over \ell }$$
B
$${3 \over 7}{v \over \ell }$$
C
$${3 \over {7\sqrt 2 }}{v \over \ell }$$
D
$${4 \over 7}{v \over \ell }$$
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